Ontologies are at the heart of the Semantic Web technologies. This paper introduces a framework for reasoning under uncertainty in the context of ontologies represented in description logics; these ontologies could be inconsistent or incoherent. Conflicts are addressed through a form of logic-based argumentation. We examine how the number of attacks and the weights of arguments can be used to define various labelling functions that identify the justification statuses of arguments. Then, different inference relations are distinguished to obtain meaningful answers to queries from imperfect ontologies without extra computational costs compared to classical DL reasoning. Lastly, we study the properties of these new entailment relations and their relationships with other well-known existing ones.
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